Name: _______________________________________________________
Due: Tuesday, June 10th
Ms. Kinzer
Project Regents: Answer all 78 questions below. Show all work on this exam. You will get 78 points for completing all
multiple choice questions and 22 points for defining or listing 22 important algebra words, concepts, rules, or formulas that
you used while completing this project, or that you think you will need to use on the Integrated Algebra Regents exam on
June 20th.
PART I
1 Which expression represents “5 less than twice x”?
1)
2)
3)
4)
4 If the point
equation
1) 1
2) 2
3)
4)
2 Gabriella has 20 quarters, 15 dimes, 7 nickels, and
8 pennies in a jar. After taking 6 quarters out of
the jar, what will be the probability of Gabriella
randomly selecting a quarter from the coins left in
the jar?
lies on the line represented by the
, the value of k is
5 A soda container holds
gallons of soda. How
many ounces of soda does this container hold?
1)
2)
1)
2)
3)
4)
3)
4)
6 The roots of a quadratic equation can be found
using the graph below.
3 Based on the line of best fit drawn below, which
value could be expected for the data in June 2015?
1)
2)
3)
4)
44
176
640
704
230
310
480
540
What are the roots of this equation?
, only
1)
and
2)
3)
and 4
, and 4
4)
1
7 If the area of a rectangle is represented by
and its length is represented by
which expression represents the width of the
rectangle?
1)
2)
3)
4)
12 If the expression
is the value of a?
1) 12
2) 2
3) 32
4) 4
,
is equivalent to
13 Which table shows bivariate data?
8 Which set of data describes a situation that could
be classified as qualitative?
1) the colors of the birds at the city zoo
2) the shoe size of the zookeepers at the city zoo
3) the heights of the giraffes at the city zoo
4) the weights of the monkeys at the city zoo
is
9 The value of the expression
1)
2)
3)
4)
1)
50
102
740
750
2)
10 Which interval notation represents
1)
2)
3)
4)
11 The solutions of
and
1)
2) 2 and 14
and
3)
4) 4 and 7
?
3)
are
4)
2
, what
18 Which type of function is graphed below?
14 The box-and-whisker plot below represents the
results of tests scores in a math class.
What do the scores 65, 85, and 100 represent?
, median,
1)
2)
, , maximum
3) median, , maximum
4) minimum, median, maximum
15 The expression
1)
2)
3)
4)
is undefined when the value
of x is
1)
, only
and 3
2)
3) 3, only
and 2
4)
19 What is the slope of the line represented by the
?
equation
1)
2)
16 If
, which expression represents x?
3)
1)
4)
2)
3)
4)
17 What is the solution of the equation
1)
2)
3)
4)
linear
quadratic
exponential
absolute value
?
1 and
2 and
and 8
and 4
3
23 Which expression represents the number of hours
in w weeks and d days?
1)
2)
3)
4)
20 The diagram below shows the graph of which
inequality?
24 Given:
What is
1)
2)
3)
4)
1)
2)
3)
4)
25 Which equation could be used to find the measure
of angle D in the right triangle shown in the
diagram below?
21 Carol plans to sell twice as many magazine
subscriptions as Jennifer. If Carol and Jennifer
need to sell at least 90 subscriptions in all, which
inequality could be used to determine how many
subscriptions, x, Jennifer needs to sell?
1)
2)
3)
4)
1)
22 When
the result is
1)
2)
3)
4)
is subtracted from
?
,
2)
3)
4)
4
26 If the roots of a quadratic equation are
the equation can be written as
1)
2)
3)
4)
and 3,
31 Solve the inequality
x.
algebraically for
32 Oatmeal is packaged in a cylindrical container, as
shown in the diagram below.
27 Which equation represents a line that is parallel to
?
the y-axis and passes through the point
1)
2)
3)
4)
28 There are 18 students in a class. Each day, the
teacher randomly selects three students to assist in
a game: a leader, a recorder, and a timekeeper. In
how many possible ways can the jobs be assigned?
1) 306
2) 816
3) 4896
4) 5832
The diameter of the container is 13 centimeters and
its height is 24 centimeters. Determine, in terms of
S, the volume of the cylinder, in cubic centimeters.
33 The distance from Earth to Mars is 136,000,000
miles. A spaceship travels at 31,000 miles per
hour. Determine, to the nearest day, how long it
will take the spaceship to reach Mars.
29 In triangle RST, angle R is a right angle. If
and
, what is the length of ?
1) 10
2) 2
3)
4)
30 How many solutions are there for the following
system of equations?
1)
2)
3)
4)
1
2
3
0
5
34 The menu for the high school cafeteria is shown
below.
38 A jar contains five red marbles and three green
marbles. A marble is drawn at random and not
replaced. A second marble is then drawn from the
jar. Find the probability that the first marble is red
and the second marble is green. Find the
probability that both marbles are red. Find the
probability that both marbles are the same color.
39 In the diagram below of rectangle AFEB and a
,
inches,
semicircle with diameter
, and
inches. Find the
area of the shaded region, to the nearest hundredth
of a square inch.
Determine the number of possible meals consisting
of a main course, a vegetable, a dessert, and a
beverage that can be selected from the menu.
Determine how many of these meals will include
chicken tenders. If a student chooses pizza, corn or
carrots, a dessert, and a beverage from the menu,
determine the number of possible meals that can be
selected.
35 A man standing on level ground is 1000 feet away
from the base of a 350-foot-tall building. Find, to
the nearest degree, the measure of the angle of
elevation to the top of the building from the point
on the ground where the man is standing.
36 Express
radical form.
in simplest
37 Solve algebraically:
[Only an algebraic solution can receive full credit.]
6
PART II
1 A system of equations is graphed on the set of axes
below.
The solution of this system is
1) (0, 4)
2) (2, 4)
3) (4, 2)
4) (8, 0)
2 A cell phone can receive 120 messages per minute.
At this rate, how many messages can the phone
receive in 150 seconds?
1) 48
2) 75
3) 300
4) 18,000
3 The value of y in the equation
0.06y + 200 = 0.03y + 350 is
1) 500
2) 1, 666. 6
3) 5,000
4) 18, 333. 3
4 The scatter plot shown below represents a
relationship between x and y.
This type of relationship is
1) a positive correlation
2) a negative correlation
3) a zero correlation
4) not able to be determined
5 The sum of 3x 2 + 5x − 6 and −x 2 + 3x + 9 is
1) 2x 2 + 8x − 15
2) 2x 2 + 8x + 3
3) 2x 4 + 8x 2 + 3
4) 4x 2 + 2x − 15
6 Jason’s part-time job pays him $155 a week. If he
has already saved $375, what is the minimum
number of weeks he needs to work in order to have
enough money to buy a dirt bike for $900?
1) 8
2) 9
3) 3
4) 4
7 The expression 9a 2 − 64b 2 is equivalent to
1) (9a − 8b)(a + 8b)
2) (9a − 8b)(a − 8b)
3) (3a − 8b)(3a + 8b)
4) (3a − 8b)(3a − 8b)
8 The scatter plot below shows the profit, by month,
for a new company for the first year of operation.
Kate drew a line of best fit, as shown in the
diagram.
12 The length of a rectangle is 15 and its width is w.
The perimeter of the rectangle is, at most, 50.
Which inequality can be used to find the longest
possible width?
1) 30 + 2w < 50
2) 30 + 2w ≤ 50
3) 30 + 2w > 50
4) 30 + 2w ≥ 50
13 Craig sees an advertisement for a car in a
newspaper. Which information would not be
classified as quantitative?
1) the cost of the car
2) the car’s mileage
3) the model of the car
4) the weight of the car
Using this line, what is the best estimate for profit
in the 18th month?
1) $35,000
2) $37,750
3) $42,500
4) $45,000
14 What are the coordinates of the vertex and the
equation of the axis of symmetry of the parabola
shown in the graph below?
9 Which statement illustrates the additive identity
property?
1) 6 + 0 = 6
2) −6 + 6 = 0
3) 4(6 + 3) = 4(6) + 4(3)
4) (4 + 6) + 3 = 4 + (6 + 3)
10 Peter walked 8,900 feet from home to school.
How far, to the nearest tenth of a mile, did he
walk?
1) 0.5
2) 0.6
3) 1.6
4) 1.7
1)
2)
3)
4)
11 Is the equation A = 21000(1 − 0.12) t a model of
exponential growth or exponential decay, and what
is the rate (percent) of change per time period?
1) exponential growth and 12%
2) exponential growth and 88%
3) exponential decay and 12%
4) exponential decay and 88%
(0, 2) and y = 2
(0, 2) and x = 2
(−2, 6) and y = −2
(−2, 6) and x = −2
15 A correct translation of “six less than twice the
value of x” is
1) 2x < 6
2) 2x − 6
3) 6 < 2x
4) 6 − 2x
2
16 The rectangular prism shown below has a length of
3.0 cm, a width of 2.2 cm, and a height of 7.5 cm.
| 4(−6) + 18
20 What is the value of ||
4!
|
1) 1
4
2) − 1
4
3) 12
4) −12
|
|?
||
21 Given: A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {2, 3, 5, 7}
What is the surface area, in square centimeters?
1) 45.6
2) 49.5
3) 78.0
4) 91.2
D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What statement is false?
1) A ∪ B ∪ C = D
2) A ∩ B ∩ C = { }
3) A ∪ C = {1, 2, 3, 5, 7}
4) A ∩ C = {3, 5, 7}
17 Which set of coordinates is a solution of the
equation 2x − y = 11?
1) (−6, 1)
2) (−1, 9)
3) (0, 11)
4) (2, −7)
22 Which expression is equivalent to
2x 6 − 18x 4 + 2x 2
?
2x 2
1)
2)
3)
4)
18 The graph of a parabola is represented by the
equation y = ax 2 where a is a positive integer. If a
is multiplied by 2, the new parabola will become
1) narrower and open downward
2) narrower and open upward
3) wider and open downward
4) wider and open upward
x 3 − 9x 2
x 4 − 9x 2
x 3 − 9x 2 + 1`
x 4 − 9x 2 + 1
23 In a given linear equation, the value of the
independent variable decreases at a constant rate
while the value of the dependent variable increases
at a constant rate. The slope of this line is
1) positive
2) negative
3) zero
4) undefined
19 Which equation represents a line that has a slope of
3
and passes through the point (2, 1)?
4
1) 3y = 4x − 5
2) 3y = 4x + 2
3) 4y = 3x − 2
4) 4y = 3x + 5
24 The volume of a cylindrical can in 32π cubic
inches. If the height of the can is 2 inches, what is
its radius, in inches?
1) 8
2) 2
3) 16
4) 4
3
29 The probability it will rain tomorrow is 1 . The
2
probability that our team will win tomorrow’s
basketball game is 3 . Which expression
5
represents the probability that it will rain and that
our team will not win the game?
1) 1 + 3
2 5
2) 1 + 2
2 5
3) 1 × 3
2 5
4) 1 × 2
2 5
25 The expression 142 + x is undefined when x is
x −4
1) −14, only
2) 2, only
3) −2 or 2
4) −14, −2, or 2
26 What is the solution of
1)
2)
3)
4)
−1 and −3
−1 and 3
1 and −3
1 and 3
x+1
2
=
?
2
x+1
27 The total score in a football game was 72 points.
The winning team scored 12 points more than the
losing team. How many points did the winning
team score?
1) 30
2) 42
3) 54
4) 60
30 The formula for the volume of a pyramid is
1
V = Bh. What is h expressed in terms of B and
3
V?
1) h = 1 VB
3
2) h = V
3B
3) h = 3V
B
4) h = 3VB
28 What is the perimeter of the figure shown below,
which consists of an isosceles trapezoid and a
semicircle?
31 State the value of the expression
(4.1 × 10 2 )(2.4 × 10 3 )
(1.5 × 10 7 )
1)
2)
3)
4)
in scientific notation.
32 Express the product of x + 2 and 24x + 20 in
2
x + 6x + 8
simplest form.
20 + 3π
20 + 6π
26 + 3π
26 + 6π
4
34 The following cumulative frequency histogram
shows the distances swimmers completed in a
recent swim test.
33 On the set of axes below, graph y = 3 x over the
interval −1 ≤ x ≤ 2.
Based on the cumulative frequency histogram,
determine the number of swimmers who swam
between 200 and 249 yards. Determine the number
of swimmers who swam between 150 and 199
yards. Determine the number of swimmers who
took the swim test.
35 Ashley measured the dimensions of a rectangular
prism to be 6 cm by 10 cm by 1.5 cm. The actual
dimensions are 5.9 cm by 10.3 cm by 1.7 cm.
Determine the relative error, to the nearest
thousandth, in calculating the volume of the prism.
36 Solve the following system of equations
algebraically for all values of x and y.
y = x 2 + 2x − 8
y = 2x + 1
5
37 A company is running a contest and offering a first,
second, and third prize. First prize is a choice of a
car or $15,000 cash. Second prize is a choice of a
motorbike, a trip to New York City, or $2,000 cash.
Third prize is a choice of a television or $500 cash.
If each prize is equally likely to be selected, list the
sample space or draw a tree diagram of all possible
different outcomes of first, second, and third prizes.
Determine the number of ways that all three prizes
selected could be cash. Determine the number of
ways that none of the three prizes selected could be
cash.
39 On the set of axes below, graph the following
system of inequalities.
y+x≥3
5x − 2y > 10
State the coordinates of one point that satisfies
y + x ≥ 3, but does not satisfy 5x − 2y > 10.
38 In right triangle ABC shown below, AC = 29
inches, AB = 17 inches, and m∠ABC = 90. Find
the number of degrees in the measure of angle
BAC, to the nearest degree.
Find the length of BC to the nearest inch.
6